Digital audio systems are well known in the prior art. Presently, two types of digital audio systems, the compact disc ("CD") and the digital audio tape ("DAT"), are enjoying commercial success as mass production audio reproduction systems. Digital audio systems have attracted critical listeners of professional or high-end analog systems.
The goal of any digital audio system is to sample and to reconstruct an analog audio signal, without noticeable changes to the signal, which will recreate authentic sounding music. If, for example, the audio signal is sampled at a recording studio and the digital samples are stored on a CD, then the CD player must retrieve the digital samples and reconstruct the waveform of the audio signal as closely as possible to the waveform of the original analog signal.
In theory, the sampling rate of a digital audio system is governed by the Nyquist Theorem that any signal may be sampled and reconstructed, provided the sampling rate is at least twice the highest frequency component of the original analog signal. An insufficiently high sampling rate tends to create an overlap in the reconstructed signal that gives rise to a special form of distortion known as aliasing. When the sampling rate is too low, the frequency domain images of the reconstructed signal overlap with the baseband and corrupt the higher frequency components of the baseband. Avoidance of aliasing is a primary goal of the sampling process of a digital audio system.
Because human hearing is usually considered to be bandlimited to 20 KHz, some prior art digital audio systems have proposed that a 20 KHz bandwidth is sufficient for high quality and audio reproduction systems. The 20 KHz is based partly on tests where a subject is instructed to listen to a sinusoidal waveform that continuously increases in frequency and to determine when the signal becomes inaudible. Most people will not be able to detect such a signal once it reaches 20 KHz. The audio bandwidth of current CD systems is 20 KHz and the guard band is 2 KHz. Therefore, the digital sampling rate, in accordance with the Nyquist Theorem, is 44.1 KHz.
Transients are necessary for professional and high-end audio reproduction because they are important to human hearing in the reconstruction of wavefronts that yield the three-dimensional ambience associated with stereophonic signals. To most listeners of professional or high-end audio systems, it is critical that the reproduced music possesses this three-dimensional ambience where each individual sound source is perceived as being located on an imaginary sound stage. Indeed, the illusion of a stable three-dimensional sound image is the fundamental feature on which stereo sound is predicated.
Transients are also important in the resolution of the individual nuances of each of the sound sources. Natural music consists of characteristic noises and momentary silences between notes or overtone oscillations. It is important to prevent sonic blurring of these subtle nuances in the program material. Such details are easily destroyed by audio systems with poor transient response or excessive thermal noise and distortion, with the reproduced music sounding muddy and devoid of fine detail.
Currently, to reproduce high frequency transient signals in current digital audio systems, frequency domain brickwall filters are used to smooth the digital samples during the reconstruction of the analog audio signal. Theoretically, a frequency domain method of digital audio signal reconstruction should work if the low pass brickwall filter could ideally pass all signals below its threshold or roll-off frequency at unitary gain and reject all signals above its roll-off frequency, and if the distance between the digital sample points is small enough that information is not lost during the sampling process. Unfortunately, an ideal low pass filter cannot be realized for the real world of dynamic music material. It is possible to create a low pass brickwall filter that has excellent frequency domain specifications when driven by constant-energy-envelope sinusoids. When this brickwall or taut filter is driven by the transients and impulses of dynamic music material, it generates overshoot, ripple and ringing.
FIG. 8A shows the frequency response of a brickwall filter. The brickwall filter approximates an ideal low pass filter. The advantages of the brickwall filter are that it has a relatively flat passband 54. It has a steep transition band 56 and a stop band 58 that provides good image rejection.
Brickwall filters have two negative characteristics. First, brickwall filters inherently have small amplitude ripples 60 in the passband 54 caused by the steep transition band 56 (as shown in FIG. 8A).
This passband ripple 60 causes an echo in the impulse response which is one of the contributors of Digital Time Displacement Error ("TDE"). The amplitude of these echoes is directly proportional to the amplitude of the passband ripples. This echo limits the resolution of the transient signals because the digital filter echo is the limiting factor in specifying realizable bits of transient resolution.
Second, the steep transition band in a brickwall filter causes time domain ripples in response to transients and impulses. These time domain ripples are another contributor to TDE.
FIG. 8B shows the frequency response of a monotonic filter. The monotonic filter is characterized by the wide transition band 56. One advantage of the monotonic filter is that it does not produce an echo. Another advantage of the monotonic filter is that it has a better impulse response (which models a transient signal) than a brickwall filter. The monotonic filter has a good impulse response because of its wide transition band, i.e., the slow roll-off, which can be a drop off of 6 dB at half the sampling rate.
However, the monotonic filter has an image energy problem. It makes a high frequency sine wave look like it has a beat because it has a poor stop band performance.
It has been recognized that a digital filter could be used in signal reconstruction to perform "oversampling". The basic idea of the prior art oversampling techniques was to implement a digital low pass filter to carry out the function of the analog brickwall smoothing filters, with samples retrieved from the digital low pass filter at the higher oversampling rate.
To improve over frequency domain digital oversampling filters, it was proposed in U.S. Pat. No. 5,075,880 to Moses to perform the filtering function by working in the time domain and using interpolation techniques to reconstruct digital audio signals.
It has been recognized, however, that digital interpolation filters with either brickwall or with monotonic configurations have limitations. Neither is ideal for all types of signals. Brickwall filters have echo and introduce ringing artifacts into music due to their abrupt cut-off. Monotonic filters typically have level-drop at the highest passband frequencies and poor rejection of images.
What is needed is a digital filter that overcomes the disadvantages of having to use either a brickwall filter or a monotonic filter.